Question

A sample contains $10^{-2} \,kg$ each of the two substances $A$ and $B$ with half-lives $4s$ and $8 s$ respectively. Their atomic weights are in the ratio of $1 : 2$, the amounts of $A$ and $B$ after an interval of $16 s$ are

• A. $A= 0.625 \times10^{-4} kg, B =0.25 \times10^{-3} kg$
• B. $A= 0.25 \times 10^{-3} kg, B =0.625 \times10^{-4} kg$
• C. $A= 2.5 \times 10^{-3} kg, B =6.25 \times 10^{-4} kg$
• D. $A= 6.25 \times 10^{-4} kg, B =2.5 \times 10^{-3} kg$

Answer 1

Answer: (D)

The amount left after $N$ half-lives
$N=N_{0}\left[\frac{1}{2}\right]^{n}$
For A , $n =\frac{t}{T_{\frac{1}{2}}}=\frac{16 s }{4 s }=4 $
$N_{A} =10^{-2} kg \left[\frac{1}{2}\right]^{4}=6.25 \times 10^{-4} \,kg$
For B, $n =\frac{16 s }{8 s }=2 $
$N_{B} =10^{-2} kg \left[\frac{1}{2}\right]^{2}$
$=2.5 \times 10^{-3} \,kg$